Multiple interacting circular nano-inhomogeneities with surface/interface effects
- 作者：Sofia G. Mogilevskaya ; Steven L. Crouch ; Henryk K. Stolarski
- 关键词：Nano-inhomogeneity ; Gurtin and Murdoch model ; Surface elasticity ; Surface tension ; Boundary integral equations
- 刊名：Journal of the Mechanics and Physics of Solids
- 出版年：2008
- 期刊代码：111_00225096
- 类别：et
- 出版时间：June 2008
- 卷：56
- 期：6
- 页码：2298-2327
- 文件大小：3474 K
摘要
A two-dimensional problem of multiple interacting circular nano-inhomogeneities or/and nano-pores is considered. The analysis is based on the Gurtin and Murdoch model [Gurtin, M.E., Murdoch, A.I., 1975. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323.] in which the interfaces between the nano-inhomogeneities and the matrix are regarded as material surfaces that possess their own mechanical properties and surface tension. The precise component forms of Gurtin and Murdoch's three-dimensional equations are derived for interfaces of arbitrary shape to provide a basis for critical review of various modifications used in the literature. The two-dimensional specification of these equations is considered and their representation in terms of complex variables is provided. A semi-analytical method is proposed to solve the problem. Solutions to several example problems are presented to: (i) examine the difference between the results obtained with the original and modified Gurtin and Murdoch's equations, (ii) compare the results obtained using Gurtin and Murdoch's model and those for a problem of nano-inhomogeneities with thin membrane-type interphase layers, and (iii) demonstrate the effectiveness of the approach in solving problems with multiple nano-inhomogeneities.